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Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 202v

Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German. Mean line confidence on this page: 0.85.

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The machine reads it as

  1. pportet ut progressio replicata sit talis, ut in casu indefiniti, sc termira-
  2. r.g. in progo Arithm. est 2(y) = y + (y) in Geometria Vy(y) = (y) et
  3. in Harmonica 2bd= (y) = 2y(y) :, y +(y)
  4. in antiharmonica (y) = yy = (73(y) _3: y +y)
  5. Q vitendum qu sic si sit 2 (y) (y) = yy + (y)1(7)
  6. quando in serre pb aliquid invenirigstans, ses est non parvi momenti ad
  7. ravemiendcto melius progessione
  8. y- (7) = (y) -(y))
  9. sie in Arithmetica est
  10. = = - 1
  11. in Harmonica Z e (yD
  12. (y)
  13. 1s
  14. (X (y): y = (y): y)
  15. quid si y(y) = (7) (y) hioc non procedit, jam in terminatione fieret jus consa
  16. in Gcometrica
  17. ergo revera esset ad rectam axi parallelam.
  18. :y constans.
  19. Si (1) + e quid si (+ a, (y) + a, : y constans = r fit yY - (y) = a
  20. (y) + y 3 : 3)
  21. 14β et (y)C y + dy sit (d +) B ( 9 dy = a seu dy sed
  22. gy (y) (y) - (9 ) = (9) (y) = yy. . Est series cujus termino
  23. sed jam tum patet hinc non posse fieri lineam
  24. (udas set 1
  25. num quorum quadrati sunt progressionis authmeticae qui sunt scilicet sax =y
  26. go yy _
  27. (y) seu (y) +93 :y = constanti habet
  28. quidem hoc ut ferminis lineae consentiat seu ut succedat aequatio, si y, (y), (sY
  29. aequalio, (y) +4.: Y. = CyY +p
  30. aequales. Sid non sucerat Uex differentialium seu 1d9) Y dus
  31. eaum
  32. C uode non p fieri dus infinite parva, un si cum
  33. gy + (y) y) _: 2 y (y) =, X fiet (y y + yyrt rydy + dydy = (299 + 2ydy
  34. y
  35. umigordinatae f 2y() = aa
  36. y4 dy 4 a,=
  37. fiet dudis =0. Erguu constans
  38. yrydys + dy dy-gy fit 29 dy = rax. seu
  39. et ergo hoc fldorema oq punctum curvam
  40. S
  41. y(y)= yy = rdx seu
  42. cura noluquacrum series habet hoc ut si ut ex tribus componatur aliquid
  43. constan aequalie nihulo non ex duob,s cum latera loscuplorum quadcati,
  44. fiet yy = LYX
  45. octanguli, ibguti sunt +E. A2 - M) H(2 - + (2 - +2)) etc. et lctum polygonam
  46. +299 5 +da Ergo salle
  47. =f+ df fit 25F4 255 + dfdf 2 af + aa
  48. cirpumferentia suut A, B, C inveni et A: B = f, et B: C = g.
  49. tam rationum datu sehies sit
  50. quod hon licet applicare ad euibo
  51. in curva rel nteriorem, ubi recomnis
  52. escenditur abesse coa abscissa cum suns
  53. tune liceret. Minuere
  54. Numerum quarrando
  55. scissaru, tunquam novu termitum
  56. reduco pt ad rabdals ordut
  57. b

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 202v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068198:0404?run=74